Yes they have. Driving through Udaipur even to reach hotel will be challenging though due to narrow lanes.
contact hotel reception to double check; should be possible....
Yes they do have a small parking space provided they don't already have a cars parked outside.
Yes they have a medium sized parking area in the hotel as well as there is space outside the hotel too to park the car . Security guard is positioned at the hotel gate .
Get an answer from Lake Pichola Hotel staff and past guests.